General noise protection measures

To reduce the transmission of sound along an airborne sound path between a noise source and a receiver, structural sound barriers – or partitions – are commonly installed between the source and the receiver [6]. An example is shown in Fig. 1.1 for an aircraft with CROR engines mounted at the rear end of the fuselage. In order to reduce the amount of noise impinging the fuselage, a noise shield acting as a sound barrier can be installed near the engines. The purpose is to block a significant amount of sound energy and thus reduce the noise transmitted into the cabin via the fuselage. In general, the sound power transmitted through a partition is attenuated by a combination of three different physical mechanisms [79]: (1) partial reflection of the incoming sound waves due to sudden changes of acoustic impedance across the partition, (2) absorption of acoustic energy by the dissipative conversion of kinetic energy into heat inside the partition, and (3) redirection of sound as structure-borne sound into flanking parts. In many cases, the latter sound reduction mechanism is undesired, since the redirected structure-borne sound waves can radiate sound at different locations (e.g. into the aircraft cabin in Fig. 1.1). Hence, most noise barrier technologies rely on a combination of sound reflection and absorption [22].

Figure 1.1: Noise shield for an aircraft with CROR engines.

The sound reduction of a partition is quantified by thesound power transmission coefficient τ. In general,τ is a frequency dependent quan-tity and defined as the ratio of the transmitted sound powerW_t to the incident sound powerWi[22]:

τ = W_t Wi

. (1.1)

Commonly, the sound power transmission coefficient is represented in logarithmic form as the so-called transmission loss TL, given by

TL =−10 lgτ (1.2) in dB. Apart from the frequency, the sound transmission through a partition also depends on other properties of the incident sound field, e.g. if it is characterized by a single normally or obliquely incident plane wave, a diffuse sound field, or a field incidence sound field [6].

The simplest type of partition is a single homogeneous wall. Assum-ing a limp unbounded wall (i.e. bendAssum-ing stiffness, boundary conditions, and low-order eigenmodes of the wall are neglected) and the same fluid on both sides of the wall, the normal incidence sound transmission coefficientτ is given by [6]

τ =

−1, ω = 2πf is the angular frequency, m⁰⁰ is the surface mass density of the wall, andρ0 and c0 are the mass density and the speed of sound of the surrounding fluid, respectively. Consequently, the normal incidence sound transmission loss of the wall is

TL = 20 lg

which is commonly known as the mass-law transmission loss. From Eq. (1.4) it is evident that for a single wall partition with ωm⁰⁰ 2ρ₀c₀the transmission loss increases by 6 dB per doubling of frequency or surface mass density. Consequently, mass-law dominated partitions must be rather heavy in order to provide a reasonable sound reduction in the low-frequency regime.

A common method for increasing the sound transmission loss of a partition is to use a so-called double wall arrangement, as shown in Fig. 1.2(a). In a double wall, two walls with surface mass densities m⁰⁰₁ andm⁰⁰₂ are separated by an air gap of heightd. The qualitative normal incidence sound transmission loss spectrum of an idealized double wall with two homogeneous unbounded walls and no mechanical connec-tion between these walls is shown for two different cases in Fig. 1.2(b):

The solid line represents the TL of a double wall without any further treatment of the air gap between the two walls. The dashed line shows the transmission loss of a double wall with an air gap filled by sound absorbing material (e.g. glass wool) to reduce the acoustic coupling

be-d m⁰⁰1

m⁰⁰2

(a) Double wall.

lgf

fd1

TL

Single wall Double wall

Double wall (with absorption)

fd2fd3

f0

6 dB/Oct.

18dB/Oct.

(b)Transmission loss.

Figure 1.2: Typical normal incidence sound transmission loss spectrum of a double wall with and without absorbing material inside the air gap (b), as shown in (a).

tween the two walls. In addition to this, the mass-law transmission loss of a single wall with equal total mass is shown in Fig. 1.2(b) for com-parison. For very low frequencies, the transmission loss of the double wall follows the mass-law relationship with the surface mass densities of the two walls combined. At a certain frequency, denoted by f₀ in Fig. 1.2(b), the double wall transmission loss is considerably reduced.

This reduction corresponds to the mass-air-mass resonance mode of the double wall system, where the two walls act as masses connected by an air spring. In case of an oblique plane wave with incidence angleθ_i, the mass-air-mass resonance frequency is given by [57]

f0= 1 2πcosθ_i

s ρ0c²₀

d

m⁰⁰₁+m⁰⁰₂

m⁰⁰₁m⁰⁰₂ . (1.5) For frequencies greater thanf₀, the double wall arrangement exhibits a clear transmission loss improvement over the mass equivalent single wall with TL increasing by up to 18 dB per octave [22]. Thus, the wall spacing d and/or wall masses need to be chosen sufficiently large in order to achieve a benefit over the transmission loss of a single wall with equivalent surface mass density in the low-frequency regime. By this means, the mass-air-mass resonance frequency, as given by Eq. (1.5), is shifted below the lowest frequency of interest. Hence, lightweight double wall constructions for low-frequency noise protection require very large wall spacings, which can be difficult to realize in certain cases where the available installation space for noise protection is strongly limited.

Double walls can be found around the passenger cabins of aircraft, where the fuselage skin with the attached stiffeners and the interior trim panels represent the two walls. The air gap is filled with glass wool for thermal and noise insulation purposes [14, 60, 102]. Typically, the wall spacing is predetermined by the height of the frame stiffeners.

Hence, there usually is little to no room for shifting the mass-air-mass resonance frequency to lower frequencies by increasing the wall spacing.

As a result, higher panel masses are required in order to improve the low-frequency noise reduction of aircraft cabin sidewalls in the form of a conventional double wall design, leading to unacceptably high weight penalties for commercial aircraft [78, 103]. There have been several efforts in the past for improving the low-frequency sound transmission loss of double walls without changing the air gap height or panel masses, e.g. by integrating acoustic resonators between the walls [37, 57, 75] or using dynamic vibration absorbers mounted onto the fuselage [91, 102].

The general effect of sound absorbing material added inside the air gap can be seen in Fig. 1.2(b) by comparing the black solid curve (no absorbing material) with the dashed curve (with absorbing material).

The absorbing material is most effective at the resonance frequencies, where airborne coupling between the walls is strong. Furthermore, the addition of sound absorbing materials becomes even more beneficial when oblique and diffuse sound fields are propagating through the dou-ble wall, because of the increased path length of oblique waves passing through the cavity [22]. Therefore, air gaps inside double walls should be treated with as much absorbing material as possible.

Probably the most widely used sound absorbing materials are porous materials (e.g. melamine foam or glass wool). The primary energy dis-sipation mechanism in these materials is the conversion of acoustical kinetic energy into heat due to viscous losses. Since viscous forces in linear harmonic dynamic systems are proportional to the frequencyf, porous absorbers are particularly efficient at medium to high frequen-cies, whereas the absorption of these materials at frequencies below 250. . .500 Hz is rather poor [24]. This, however, can be improved by increasing the thickness of the absorber material or mounting a sheet of absorbing material a 1/4-wavelength apart from a reflecting surface [50]. But since the wavelength of low-frequency acoustic waves in air is typically >1 m, porous absorbers are rarely used for low-frequency sound absorption.

The low-frequency performance of an acoustic absorber can be im-proved by increasing the energy density of the system. So-called reso-nance absorbers combine the significantly increased energy density at the resonance frequency of a dynamic system with a damping mech-anism (e.g. internal losses inside a flexing plate). Thus, a greatly im-proved sound absorption in a frequency band around the resonance frequency can be obtained. Widely used resonance absorbers are, for example, Helmholtz resonators or micro-perforated panels (MPPs) and plate or foil absorbers. The resonant system of Helmholtz resonators and MPPs is composed of the mass of a small air volume in the neck of the resonator and the compliance of a larger air volume enclosed by the resonator. In case of the plate or foil absorbers, the mass of the plate/foil is backed by a compliant air cavity and damping is achieved through the internal losses inside the plate/foil materials [94]. While these absorber types are particularly efficient at low frequencies, their bandwidth is relatively narrow. Only particular tonal components in the noise spectrum can be filtered out unless combinations of resonance absorbers with different properties are employed to achieve a broader sound absorption.

Resonance absorbers have been frequently used in low-frequency noise control problems. As mentioned above, Helmholtz resonators have been used to increase the low-frequency transmission loss of aircraft cabin side walls [37, 57, 75]. Helmholtz resonators have also been em-ployed inside launch vehicle payload fairings in order to protect the pay-load from excessive low-frequency sound pressure levels during launch [8, 19, 20]. For a similar application, Kidner et al. [33] investigated the enhanced low-frequency noise reduction of poro-elastic layers with randomly embedded masses.

Apart from the passive noise reduction technologies described in this section, numerous active low-frequency noise and vibration con-trol techniques have also been investigated and successfully realized

[14, 17, 25, 76], e.g. in the cabin of the propeller-driven Saab 2000 aircraft [18] or the loadmaster area of the A400M military transporter [34]. While being clearly effective, especially in the low-frequency range, these active technologies require a certain amount of sensors, actuators, control architecture, and cables. This electrical infrastructure can add up to a significant amount of weight and maintenance effort, espe-cially for multi-input and multi-output control systems [25]. Therefore, passive noise protection measures are often preferred by the indus-try if the acoustic efficiency is comparable. The recently developed so-called acoustic metamaterials could provide the basis for new pas-sive noise control technologies with enhanced acoustic performance and lightweight capabilities.